The right way is the way it is done at a particular dojo, and the best explanation for anything like this is: because that is is the way it is done at a particular dojo.

At my dojo, our standards of etiquette require that students put their bokken on their right-hand side with the blade facing towards them, like a couple others in this thread. I have also heard that this is considered to be a less threatening / lower trust posture because it would be more difficult to draw a real sword. One of Ikeda Sensei's tapes dramatized this concept.

Though it seems to me that sword on your right side, blade facing AWAY from you would make it slightly more complicated to draw on someone, because you'd have to twist the thing to get the blade on top as you passed it to your lefthand side.

Though having your blade facing the guy next to you is not...nice in some sense. This is good example of why sometimes we just overthink things that are done simply because somebody decided to do them that way and proper students of budo default to imitating their teachers and sempai at the most minute levels without questioning.